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In a certain country, the probability of a school A topping in county exams is 1/3. If it tops the probability of it topping in...
(Solved)
In a certain country, the probability of a school A topping in county exams is 1/3. If it tops the probability of it topping in KCSE is 5/7 otherwise the probability of it topping in KCSE is 2/9. If the school tops in KCSE the probability of its appearing in the newspaper is 2/5, otherwise the probability of its appearing in newspaper is 4/11
(a) Draw a tree diagram to represent the above information
(b) Use the tree diagram to find the probability that:
(i) The school tops in the two exams and appears in the newspaper
(ii) The school did not appear in the newspaper
(iii) The school topped in at least one exam and did not appear in the newspaper
(iv) The school appeared in the newspaper
Date posted:
September 20, 2019
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Answers (1)
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A passenger plane takes off from airport A(60oN,5oE) and flies directly to another airport B(60oN,17oE) and then flies due North for 600 nautical miles (nm)...
(Solved)
A passenger plane takes off from airport A(60oN,5oE) and flies directly to another airport B(60oN,17oE) and then flies due North for 600 nautical miles (nm) another airport C
(a) Find the position of airport C
(b) Find the distance between airport A and B in nautical miles
(c) If the plane at an average speed of 300knots, find total flight time
(d)Given that the plane left air port A at 9.20am. Find the local time of arrival at airport C
Date posted:
September 20, 2019
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Answers (1)
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A solution whose volume is 120 litres is made up of 35% water and the rest alcohol. When y litres of alcohol is added the...
(Solved)
A solution whose volume is 120 litres is made up of 35% water and the rest alcohol. When y litres of alcohol is added the percentage of water drops to 15%
(a) Find the value of y
(b) The new solution is diluted further by addition of seventy litres of water. Calculate the percentage of alcohol in the resulting solution
(c) A blend is made by mixing 10 litres of the solution in (b) above with 20 liters of the original solution.
Calculate in the simplest form, the ratio of water to that of alcohol in the blend
Date posted:
September 20, 2019
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Answers (1)
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Mr. Alvin George, a civil servant gets a monthly salary of Shs. 48,000. He lives in a government house where he pays nominal rent of...
(Solved)
Mr. Alvin George, a civil servant gets a monthly salary of Shs. 48,000. He lives in a government house where he pays nominal rent of Shs.2500. Besides this he gets an automatic house allowance of Shs.12000 and medical allowance of shs.8000 per month. He gets a family relief of sh.1065 per month. The rates of income tax are shown below

Calculate:
(a) His taxable income per month in Kenya pounds
(b) Net tax per month in Kshs.
(c) Net salary
Date posted:
September 20, 2019
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Answers (1)
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A rectangle ABCD is such that AB=6cm, and BC=5cm. A variable point P moves inside the rectangle such that AP = PB and AP >2.5cm....
(Solved)
A rectangle ABCD is such that AB=6cm, and BC=5cm. A variable point P moves inside the rectangle such that AP ≤ PB and AP >2.5cm. Show the region where P lies
Date posted:
September 20, 2019
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Answers (1)
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(a) Expand and simplify the binomial expression (2x-y)5
(b) Use the first four terms of the expansion above to approximate the value of (3.8)5
(Solved)
(a) Expand and simplify the binomial expression (2x-y)5
(b) Use the first four terms of the expansion above to approximate the value of (3.8)5
Date posted:
September 20, 2019
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Answers (1)
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An arithmetic progression of 41 terms in such that the sum of the first five terms is 560 and sum of the last five terms...
(Solved)
An arithmetic progression of 41 terms in such that the sum of the first five terms is 560 and sum of the last five terms is -250. Find the first term
Date posted:
September 20, 2019
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Answers (1)
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Miss Jaber bought a motor cycle at Shs.160,000. The depreciation rate was 6% per annum determined semi annually. How long will it take the motor...
(Solved)
Miss Jaber bought a motor cycle at Shs.160,000. The depreciation rate was 6% per annum determined semi annually. How long will it take the motor cycle to be valued at a quarter of its original cost.
Date posted:
September 20, 2019
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Answers (1)
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The table below gives the income tax rates.a)Calculate income tax of Wanga’s taxable income of kshs.50,400 per monthallowing a family relief of kshs. 520 per...
(Solved)
The table below gives the income tax rates.

a)Calculate income tax of Wanga’s taxable income of kshs.50,400 per month allowing a family relief of kshs. 520 per month.
b)Calculate the total tax as a percentage of taxable income
Date posted:
September 20, 2019
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Answers (1)
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Write the expression of (2 – 1/5 x)6 up to the term in x4. Hence use the expansion to find the value of (1.96)6 correct...
(Solved)
Write the expression of (2 – 1/5 x)6 up to the term in x4. Hence use the expansion to find the value of (1.96)6 correct to 3 decimal places.
Date posted:
September 20, 2019
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Answers (1)
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The position vectors of points A and B are a = 2i + j – 8k and b = 3i +2j – 2k respectively....
(Solved)
The position vectors of points A and B are a = 2i + j – 8k and b = 3i +2j – 2k respectively. Find the magnitude of AB.
Date posted:
September 20, 2019
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Answers (1)
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A quantity P varies partly as t and partly as the square of t.When t = 20, p = 45 , and when t =...
(Solved)
A quantity P varies partly as t and partly as the square of t.When t = 20, p = 45 , and when t = 24 , p = 60.
a)Express p in terms of t.
b)Find p when t = 32.
Date posted:
September 20, 2019
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Answers (1)
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Express the recurring decimal below as a fraction; 4.372 leaving your answer in the form of a/b where a and ...
(Solved)
Express the recurring decimal below as a fraction; 4.372 leaving your answer in the form of a/b where a and b are integers.
Date posted:
September 20, 2019
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Answers (1)
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Use logarithms only to evaluate,
Correct to four significant figures.
(Solved)
Use logarithms only to evaluate,

Correct to four significant figures.
Date posted:
September 20, 2019
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Answers (1)
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(a) Complete the table below for the function:
(b) Use the mid-ordinate rule with six ordinates to estimate the area enclosed by the curve...
(Solved)
(a) Complete the table below for the function:

(b) Use the mid-ordinate rule with six ordinates to estimate the area enclosed by the curve of the functions y = x2 – 3x + 5, x – axis and the lines x = 2 and x = 8.
(c) Find the exact area of the region described in (b) above.
(d) If the mid-ordinates rule is used to estimate the area under the curve between x = 2 and x = 8, what will be the percentage error in the estimation?
Date posted:
September 20, 2019
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Answers (1)
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A farmer has at least 50 acres of land on which he plans to plant potatoes and cabbages.
Each acre of potatoes requires 6 men...
(Solved)
A farmer has at least 50 acres of land on which he plans to plant potatoes and cabbages.
Each acre of potatoes requires 6 men and each acre of cabbages requires 2 men. The farmer has 240 men available and he must plant at least 10 acres of potatoes. The profit on potatoes is Ksh. 1000 per acre and on cabbages is Ksh. 1200 per acre. If he plants x acres of potatoes and y acres of cabbages:
(a)Write down three inequalities in x and y to describe this information.
(b)Represent these inequalities graphically.
Date posted:
September 20, 2019
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Answers (1)
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In the diagram M is the midpoint of XZ. OX = p + 2q. Oz = 7p – 2q and ZY = 3Kq + Mp...
(Solved)
In the diagram M is the midpoint of XZ. OX = p + 2q. Oz = 7p – 2q and ZY = 3Kq + Mp where
k, and m are constants.

(a)Express the following in terms of p and q.
(i) XZ
(ii) XM
(iii) OM
(b)Express OY in terms of p, q, k and m.
(c)If y lies on OM produced with OY:OM = 3:2. Find the values of k and m.
Date posted:
September 20, 2019
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Answers (1)
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A blender mixes two brands of Juice A and B to obtain 70mls of the mixture worth Ksh. 165 per litre. If brand...
(Solved)
A blender mixes two brands of Juice A and B to obtain 70mls of the mixture worth Ksh. 165 per litre. If brand A is valued at Ksh. 168 per 1 litre bottle and brand B at Ksh. 153 per 1 litre bottle, calculate the ratio in which the bands A and B are mixed.
Date posted:
September 20, 2019
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Answers (1)
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A circle whose equation is (x – 1)2 + (y – k)2 = 10 passes through point (2,5). Find the coordinates of the two...
(Solved)
A circle whose equation is (x – 1)2 + (y – k)2 = 10 passes through point (2,5). Find the coordinates of the two possible centres of the circle.
Date posted:
September 20, 2019
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Answers (1)
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Use logarithm table to evaluate:
(Solved)
Use logarithm table to evaluate:

Date posted:
September 20, 2019
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Answers (1)